Static Body Conduction

Introduction

Static Body Conduction is used to model thermal conduction within static bodies embedded in the computational domain. This capability enables simulation of thermal transport through solid materials, including conjugate heat transfer interactions between solids and surrounding fluids.

The governing equation is the transient Fourier heat conduction equation

\[\frac{\partial T}{\partial t} = \alpha \nabla^2 T + \frac{\dot{q}}{\rho c_p},\]

where \(T\) is temperature, \(t\) is time, \(α\) is the thermal diffusivity, \(ρ\) is density, \(c_p\) is heat capacity, and \({\dot{q}}\) is a volumetric heat generation term. The thermal diffusivity is defined as

\[\alpha = \frac{k}{\rho c_p},\]

where \(k\) is the thermal conductivity. A key aspect of conduction modeling is the specification of thermal boundary conditions. M-Star supports both direct conduction boundary conditions and conjugate solid–fluid coupling models.

Direct conduction boundary conditions can be applied either on surfaces or within volumetric regions of the solid body. These boundary conditions directly enforce quantities such as temperature, surface heat flux, or volumetric heating terms on the conduction field.

Internal Points

Each Static Body Conduction object also requires the definition of an Internal Point. The Internal Point is analogous to the flood fill points used in fluid geometry generation—it identifies the solid conduction region from the surrounding exterior space. During geometry processing, the Internal Point allows the solver to determine which portion of the geometry should be treated as the conductive solid domain.

Internal Points are added using the Add Internal Point tool. When a Static Body Conduction object is first added to a static body, the Internal Point docked form is automatically launched to assist with initialization of the conduction region.

M-Star also supports conjugate solid–fluid thermal coupling boundary conditions. In these cases, a temperature or heat flux is not prescribed directly. Instead, the user defines a heat transfer model, typically convective in nature, that couples the solid and fluid thermal fields. The local heat transfer rate is then determined from the calculated heat transfer coefficient and the instantaneous local temperature difference between the solid and fluid regions. The resulting temperature fields evolve naturally from the coupled conductive, convective, and advective transport processes within the system.

This model can be used to investigate thermal transport through vessel walls and internal structures, conjugate heat transfer at solid–fluid boundaries, heating or cooling of immersed components, and heat diffusion within complex solid geometries.

In the example below, we model heat transfer through a jacketed vessel. The external heating jacket is represented using a surface temperature boundary condition of 400 K applied to the outside of the vessel wall. All materials are initialized at a temperature of 300 K.

Download Sample File: Static Body Conduction

Thermal energy conducts through the vessel walls according to the wall topology and the thermal properties of the solid material. On the fluid side, convective heat transfer transfers energy from the wall into the fluid. This wall-to-fluid heat transfer is modeled through the static body wall convection model, resulting in a local increase in fluid temperature near the heated surfaces.

Within the fluid, thermal energy is transported through both advection and diffusion. These transport processes are governed by the fluid flow field and the thermal properties of the fluid. The heated fluid then convects thermal energy to a submerged object, which increases in temperature as it absorbs heat from the surrounding fluid.

Property Grid

General

Conduction Mode

This setting defines how the conduction mesh is generated for the static body. In general, volume conduction is more accurate and better suited for thick solids or cases with significant internal gradients. Surface conduction is often sufficient for thin walls, shells, and sheet-like geometries.

Volume

A full 3D conduction mesh is generated throughout the interior of the static body. This approach provides the most accurate representation of thermal diffusion and internal temperature gradients.

Surface

A reduced 2D surface-based conduction model is generated using a user-defined thickness. This approach is more computationally robust and efficient for thin structures where temperature gradients through the thickness are small.

Initial Temperature

K | This defines the initial temperature field throughout the static body at the start of the simulation.

Internal Points

Point

m | These flood-fill points are used to identify the interior regions of the conduction mesh within the static body. Their placement follows the same principles as other flood-fill definitions throughout the M-Star framework. Points are added using the Add Internal Point tool.

Material

Conductivity

W/mK | This defines the thermal conductivity of the material.

Heat Capacity

J/(kgK) | This defines the material specific heat capacity.

Density

kg/m^3 | This defines the material density.

Solid Heating UDF

W/m ² or W/m ³ | This UDF defines a heating source applied uniformly over a static body surface (for 2D conduction) or volume (for 3D conduction). This capability is commonly used to model things like volumetric heat generation and resistive heating. This is a System UDF.

Download Sample File: Solid Heating

Advanced

Resolution

This defines the spatial resolution of the conduction mesh. In general, finer resolutions improve geometric fidelity and thermal gradient resolution at increased computational cost.

Auto

This automatically sets the conduction mesh resolution relative to the lattice spacing.

Custom

This allows direct specification of the conduction mesh resolution.

Dx

m | Conduction dx.

Auto Detect 2D

If enabled, the solver automatically collapses portions of the conduction mesh into a 2D representation when local geometry thickness falls below the conduction mesh resolution. This improves robustness for thin features that cannot be adequately resolved in full 3D. If disabled, all geometry must be fully resolved by the conduction mesh.

On

Auto Detect is enabled.

Off

Auto Detect is disabled.

Time Step

This defines the update frequency for solving the thermal diffusion equation.

Auto

This automatically sets the conduction solver time step relative to the simulation time step.

Custom

This allows direct specification of the conduction solver time step. Smaller conduction time steps may improve stability and temporal accuracy, while larger values can improve computational efficiency.

Dt

s | Custom time step.

Note

Temperature cannot be specified a static body thermal boundary condition if condition is enabled for that body.

Static Body Conduction Output Data

Static body conduction output data include both 3D visualization files and ASCII text files. Each static body family produces unique output files with file names linked to the dynamic name of the static body parent. The 3D visualization files are binary .pvd files used for visualization, rendering, and analysis within M-Star Post. The thermal data appended to these files can include local temperature and heat flux at the solid/liquid boundary. These visualization files are written at both the Plane/Probe Output Write Interval and the Volume Output Write Interval, allowing for concurrent animation of the thermal field with any fluid, particle, or moving body dynamics.

Static body conduction output data is also appended to the Static Body Statistics file. The ASCII text files store the time-evolution of both raw and reduced output variables. These files can be explored within M-Star Post or opened in any text editor or spreadsheet tool. The data written to these text files includes the mean solid body temperature, the total solid-liquid heat transfer rate, and the average solid-liquid heat transfer flux. These text files are updated and appended at the Statistics Write Interval. A full preview and description of the data written to these files is available in the Statistics Output Data preview panel.

Static Body Conduction Toolbar

Context-Specific Toolbar Forms	Description
Add Internal Points	The Add Internal Points form is used to add or edit internal points associated with static body condition or conduction volume boundary conditions.
Add Volume Boundary Condition	The Add Volume Boundary Condition tool imposes thermal source terms throughout a finite volume within a conducting solid.
Add Surface Boundary Condition	The Add Surface Boundary Condition tool applies thermal boundary conditions directly to the surfaces of a static body.
Help	The Help command launches the M-Star reference documentation in your web browser.

See also Child Geometry Context Specific Toolbar.

For a full description of each selection on the Context-Specific Toolbar, see Toolbar Selections.